MinT - Best Known (85−47, 85, s)-Nets in Base 64

Best Known (85−47, 85, s)-Nets in Base 64

(85−47, 85, 513)-Net over F₆₄ — Constructive and digital

Digital (38, 85, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 85, 513)-net over F₆₄, using
- net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]

(85−47, 85, 639)-Net over F₆₄ — Digital

Digital (38, 85, 639)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−47, 85, 591004)-Net in Base 64 — Upper bound on s

There is no (38, 85, 591005)-net in base 64, because

1 times m-reduction [i] would yield (38, 84, 591005)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 52 375340 414908 375808 777529 626476 914682 462221 509891 519175 120257 526928 076628 621844 013034 524513 784832 318370 433651 885516 718929 739585 884834 367905 138689 728216 > 64⁸⁴ [i]